Cycle of education: 2019/2020
Course outcomes
Speciality: Humanistic chosen module 4.1
| Symbol | Contents | Reference to the PRK learning outcomes |
|---|---|---|
| K_W01 | understands the civilizational significance of mathematics and its applications | P6S_WK |
| K_W02 | understands well the role and importance of proof in mathematics, as well as the concept of significance of assumptions | P6S_WK P6S_WG |
| K_W03 | understands the structure of mathematical theories, can use mathematical formalism to build and analyze simple mathematical models in other fields of science | P6S_WK P6S_WG |
| K_W04 | knows the basic theorems from the studied branches of mathematics | P6S_WK P6S_WG |
| K_W05 | knows the basic examples both illustrating specific mathematical concepts and allowing to refute erroneous hypotheses or unauthorized reasoning | P6S_WG |
| K_W06 | knows selected concepts and methods of mathematical logic, set theory and discrete mathematics contained in the foundations of other mathematical disciplines | P6S_WG |
| K_W07 | knows the basics of differential and integral calculus of functions of one and several variables, as well as other branches of mathematics used in it, with particular emphasis on linear algebra and topology | P6S_WG |
| K_W08 | knows the basics of computational and programming techniques that support the work of a mathematician and understands their limitations | P6S_WG |
| K_W09 | knows at basic level at least one software package, used for symbolic calculations | P6S_WG |
| K_W10 | knows at least one foreign language at intermediate level (B2) | P6S_WG |
| K_W11 | knows the basic principles of occupational health and safety | P6S_WK |
| K_U01 | is able to clearly present correct mathematical reasoning, formulate theorems and definitions in speech and writing | P6S_UK |
| K_U02 | uses the propositional and functional calculus, can correctly use quantifiers also in colloquial language | P6S_UW P6S_UU |
| K_U03 | can conduct easy and moderately difficult proofs by complete induction, he/she can define functions and recurrence relations | P6S_UW |
| K_U04 | can use a classical logic system to formalize mathematical theories | P6S_UW P6S_UK |
| K_U05 | can create new objects by constructing quotient spaces or Cartesian products | P6S_UW P6S_UK |
| K_U06 | uses the language of set theory to interpret problems relating to different branches of mathematics | P6S_UW P6S_UK |
| K_U07 | understands issues concerning different types of infinity and orders in sets | P6S_UW |
| K_U08 | can use the concept of real number; can give examples of irrational numbers and ltranscendental numbers | P6S_UW |
| K_U09 | is able to define functions, also using limits, and describe their properties | P6S_UW |
| K_U10 | can use in different contexts the concept of convergence and limit; is able to – on easy and medium difficulty levels – calculate limits of sequences and functions, determine absolute and conditional convergence of series | P6S_UW |
| K_U11 | can interpret and explain functional dependencies presented in the form of formulae, charts, graphs, schemes and apply them to practical problems | P6S_UW P6S_UO P6S_UU |
| K_U12 | can apply theorems and methods of differential calculus of functions of one and many variables to problems relating to optimization, to finding local and global extrema, and to function investigation; can give precise justification of his/her reasoning | P6S_UW |
| K_U13 | can use the definition of an integral of a function of one and several real variables; can explain analytical and geometric sense of the concept | P6S_UW |
| K_U14 | can integrate functions of one and several variables by parts and substitution; can change order of integration; can express areas of smooth surfaces and volumes in terms of integrals | P6S_UW |
| K_U15 | can apply numeric tools and methods to solving selected problems of differential and integral calculus, including those basing on its applications | P6S_UW |
| K_U16 | uses the concepts of linear space, vector, linear transformation, matrix | P6S_UW |
| K_U17 | notices algebraic structures (group, ring, field, linear space) in different mathematical issues, not necessarily associated directly with algebra | P6S_UW |
| K_U18 | can compute determinants and know their properties; can give a geometric representation of a determinant and understands its relation to mathematical analysis | P6S_UW |
| K_U19 | solves systems of linear equations with constant coefficients; can use geometric interpretation of solutions | P6S_UW |
| K_U20 | finds matrices of linear transformations with respect to different bases; computes eigenvalues and eigenvectors of matrices; can explain geometric sense of these concepts | P6S_UW |
| K_U21 | reduces matrices to a canonical form; can use this skill to solve linear differential equations with constant coefficients | P6S_UW |
| K_U22 | is able to interpret a system of ordinary differential equations in the language of geometry by means of vector field and phase space | P6S_UW |
| K_U23 | recognizes and determines the most important topological properties of subsets of Euclidean space and metric spaces | P6S_UW |
| K_U24 | applies topological properties of sets and functions to solving qualitative problems | P6S_UW |
| K_U25 | recognizes problems, including practical issues, which can be solved using algorithms; can specify this type of problem | P6S_UW P6S_UU |
| K_U26 | can construct and analyze an algorithm in accordance with a specification and write it in a selected programming language | P6S_UW |
| K_U27 | is able to compile, start and test an independently written computer program | P6S_UW |
| K_U28 | is able to use computer programs for data analysis | P6S_UW P6S_UO P6S_UK |
| K_U29 | is able to model and solve discrete problems | P6S_UW P6S_UK |
| K_U30 | uses the concept of probabilistic space; is able to construct and analyze a mathematical model of a random experiment | P6S_UW |
| K_U31 | can give various examples of discrete and continuous probability distributions and discuss selected random experiments and mathematical models in which these distributions occur; knows practical applications of basic distributions | P6S_UW P6S_UO P6S_UK P6S_UU |
| K_U32 | has ability to use formula of total probability and Bayes formula | P6S_UW |
| K_U33 | can identify parameters for the distribution of a discrete and continuous random variable; can apply limit theorems and law of large numbers to probability evaluation | P6S_UW |
| K_U34 | knows how to use statistical characteristics of a population and the sample equivalents | P6S_UW |
| K_U35 | is able to conduct simple statistical inference, also with the use of computer tools | P6S_UW P6S_UO P6S_UK |
| K_U36 | is able to present mathematical problems and issues in simple colloquial language | P6S_UW P6S_UO P6S_UK P6S_UU |
| K_K01 | knows the limitations of his/her own knowledge and understands the need for lifelong education | P6S_KK |
| K_K02 | demonstrates the ability to formulate precise questions to deepen his/her understanding of a given topic or to find missing elements of reasoning | P6S_KK P6S_KR |
| K_K03 | can interact and work in a team; understands the need of systematic work on long term | P6S_KO P6S_KR |
| K_K04 | understands the significance of intellectual honesty, both in his/her own and in other people’s activities; demonstrates ethical behavior | P6S_KK P6S_KR |
| K_K05 | understands the need to popularize selected achievements in the field of higher mathematics | P6S_KO P6S_KR |
| K_K06 | is able to obtain information from specialistic literature independently, also in foreign languages | P6S_KK |
| K_K07 | demonstrates the ability to formulate opinions concerning important mathematical issues | P6S_KK |